Marie Curie host fellowship for early stage training (EST)

Title of project:	Inverse acoustic obstacle scattering
Stipendiary: Email:	Olha Ivanyshyn ivanyshy--at--math.uni-goettingen.de
Supervisors:	Dr. Tomas Johansson and Professor Derek B. Ingham
Department:	Centre for CFD, SPEME, University of Leeds
Period:	01.07.06 to 30.09.06
EU contract no.:	MEST-CT-2005-020327

Education
2004-present	Graduate student (Graduierten kolleg "Identification in Mathematical Models"), Georg-August-University Göttingen. PhD Supervisor: Professor Dr. Rainer Kress
2002-2003	Master's degree in Applied Mathematics and Computer Science, Ivan Franko National University of Lviv. MSc Supervisor: Dozent Dr. Roman Chapko
1998-2002	Bachelor's degree in Applied Mathematics and Computer Science, Ivan Franko National University of Lviv.

Research Interests:

• Numerical Analysis
• Acoustic Scattering
• Inverse Problems

Project Area:

In many engineering applications, for example in medical imaging and non-destructive testing, a common problem is to find the shape of an unknown obstacle using information from the influence that the obstacle has on propagating waves. Such a type of problem also occurs in fluid dynamics where objects submerged in water are to be detected. A similar model can be applied when the size and shape of particles in liquid suspensions and aerosols are to be determined from light scattered by the particles. These situations can be mathematically modelled as a so-called inverse scattering problem. It is a highly challenging problem from both computational and theoretical aspects, since it is ill-posed, i.e. sensitive to errors in the data, and non-linear.

Achievements during the project:

Publications:

1. Ivanyshyn, O. and Johansson, T. (2006), Nonlinear integral equations methods for the reconstruction of an acoustically sound-soft obstacle, Journal of Integral Equations and Applications. (Submitted)

2. Ivanyshyn, O. and Johansson, T. (2006), Boundary integral equations methods for acoustical inverse sound-soft scattering, Journal of Inverse and Ill-Posed Problems. (Submitted)

Attended conferences and talks:

1. International conference on boundary element techniques (Ècole National des Ponts et Chaussées), Paris, 4 - 6 September 2006.

2. Workshop in Göttingen, 19 - 21 September 2006.
   Presentation entitled: Newton-type methods based on integral equations for inverse acoustic scattering problems.

3. Seminar in Leeds in the series "Internal Fluids and MHD Seminars", 5th October 2006.
   Presentation entitled: Newton-type methods based on integral equations for inverse acoustic scattering problems.

4. Workshop on Applied Mathematics, Linköping University, 17 - 18 October 2006.
   Presentation entitled: (shared) Non-linear integral equation methods for inverse scattering.